Extremum Seeking Control based on Numerical Optimization and State Regulation - Part I: Theory and Framework

We consider the employment of numerical optimization and state regulation to solve the extremum seeking control problem, which does not separate the dynamics from the extremum seeking loop. Extremum seeking is realized via a state regulator that drives the state traveling along a convergent set point sequence generated by a numerical optimization algorithm. In this paper, we propose a novel design of the state regulator via output tracking for state feedback linearizable systems, where the construction of reference signal and determination of regulation time are discussed in detail. We trade off the finite time state regulation to obtain flexibility in designing robust extremum seeking controller. Simulation examples are provided to show the effectiveness of the proposed scheme and illustrate some design guidelines